The `half_float` test was failing with `-mcpu=cortex-a55` (native `__fp16`) due
to a bad NaN bit-pattern comparison (in the case of casting a float to `__fp16`,
the signaling `NaN` is quieted). There was also an inconsistency between
`numeric_limits<half>::quiet_NaN()` and `NumTraits::quiet_NaN()`. Here we
correct the inconsistency and compare NaNs according to the IEEE 754
definition.
Also modified the `bfloat16_float` test to match.
Tested with `cortex-a53` and `cortex-a55`.
The existing `TensorRandom.h` implementation makes the assumption that
`half` (`bfloat16`) has a `uint16_t` member `x` (`value`), which is not
always true. This currently fails on arm64, where `x` has type `__fp16`.
Added `bit_cast` specializations to allow casting to/from `uint16_t`
for both `half` and `bfloat16`. Also added tests in
`half_float`, `bfloat16_float`, and `cxx11_tensor_random` to catch
these errors in the future.
When calling `internal::cast<S, std::complex<T>>(x)`, clang often
generates an implicit conversion warning due to an implicit cast
from type `S` to `T`. This currently affects the following tests:
- `basicstuff`
- `bfloat16_float`
- `cxx11_tensor_casts`
The implicit cast leads to widening/narrowing float conversions.
Widening warnings only seem to be generated by clang (`-Wdouble-promotion`).
To eliminate the warning, we explicitly cast the real-component first
from `S` to `T`. We also adjust tests to use `internal::cast` instead
of `static_cast` when a complex type may be involved.
If we have explicit conversion operators available (C++11) we define
explicit casts from bfloat16 to other types. If not (C++03), we don't
define conversion operators but rely on implicit conversion chains from
bfloat16 over float to other types.
Specialized `bfloat16_impl::float_to_bfloat16_rtne(float)` for normal floating point numbers, infinity and zero, in order to improve the performance of `bfloat16::bfloat16(const T&)` for integer argument types.
A reduction of more than 20% of the runtime duration of conversion from int to bfloat16 was observed, using Visual C++ 2019 on Windows 10.
Conversion from `bfloat16` to `float` and `double` is lossless. It seems natural to allow the conversion to be implicit, as the C++ language also support implicit conversion from a smaller to a larger floating point type.
Intel's OneDLL bfloat16 implementation also has an implicit `operator float()`: https://github.com/oneapi-src/oneDNN/blob/v1.5/src/common/bfloat16.hpp
